The grades on a physics midterm at Springer are normally distributed with $\mu = 80$ and $\sigma = 2.5$. Michael earned a n $87$ on the exam. Find the z-score for Michael's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Michael's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{87 - {80}}{{2.5}}} $ ${ z \approx 2.80}$ The z-score is $2.80$. In other words, Michael's score was $2.80$ standard deviations above the mean.